SOLUTION: A window is shaped like a triangular prism the side measures 18cm, 33.75 cm and 38.25 cm. a) How can we be sure that the base of this prism is a right triangular? show your work

Question 694382: A window is shaped like a triangular prism the side measures 18cm, 33.75 cm and 38.25 cm.
a) How can we be sure that the base of this prism is a right triangular? show your work.
b) What is the measure of the angle opposite the 38.25 cm side Show your work.
c) What is the measure of the angle opposite the 33.75 cm side. Show your work.
d) What is the measure of the angle opposite the 18 cm ? Show your work
can you please help me out on this question i really dont understand? thanks in advance
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
a) A triangle with sides of 18 cm, 33.75 cm, and 38.25 cm would be a right triangle if (and only if) the squares of the shorter sides add up to the square of the longer side.
Since and that triangle is a right triangle. The longest, 38.25-cm side is the hypotenuse and the other two sides are the legs of the right triangle.

Probably the terms "triangular prism", "the base of this prism" and "right triangular" (prism) confuse you.
The problem calls the window a "triangular prism" to recognize that there is some thickness to it. It seems like an excess of correctness. I bet they would correctly a coin "cylindrical" instead of "round."

b) The measure of the angle opposite the 38.25 cm is or radians. Since we proved that the triangle is a right triangle, the longest side, measuring 38.25 cm, is the hypotenuse, which is opposite the right angle.

c) The 33.75 cm side and the 18 cm sides are the legs of a right triangle.
Consequently, the tangent of the angle opposite the 33.75 cm side is the ratio of measures of opposite side, divided by adjacent side.
--> (in radians, rounded) or (rounded)

d) The 33.75 cm side and the 18 cm sides are the legs of a right triangle.
Consequently, the measures of the angles opposite those sides add up to the measure of a right angle: , or radians.
Then the measure of the angle opposite the 18 cm side is
radians (rounded)
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